Principals want foreign teachers exempted from the border ban so they can plug staffing gaps caused by the teacher shortage.
Foreign-trained teachers have been a key part of official efforts to relieve the shortage and last year nearly 1000 overseas teachers gained visas to work in New Zealand.
Secondary Principals Association president Deidre Shea said schools would normally be starting to look overseas now to fill some of next year's vacancies.
"Going forward into 2021 it's likely that we will need to employ folk from overseas in order to be sure that we get enough quality teachers into our schools," she said.
"At the moment that's not possible and that's causing some concern in some areas, where for example jobs have been offered and accepted and of course people can't travel now."
She said principals were only now starting to raise their fears about the staffing situation and they would be asking for an exemption allowing foreign-trained teachers to enter the country to take up jobs.
However, Shea said the pandemic could have positive effects on teacher supply.
"There's questions around retention of people in teaching, people perhaps returning to teaching, we have seen that before in times of recession, and whether indeed that will happen and if it does if those numbers are enough to mitigate some of the difficulties of getting folk in from overseas. So there's lots of unknowns, many more than there usually are."
Auckland Secondary Principals Association president Steve Hargreaves said the pandemic was also prompting more New Zealand teachers to return from overseas jobs.
"We at our school here advertised for an English teacher to start in term three, and two of the applicants we got were recent folks who'd come back from overseas," he said.
"Trained teachers, had planned to stay overseas for much longer, the Covid situation looked much better in New Zealand so home they came and we have managed to secure a very good English teacher because of that."
However, Hargreaves said nobody was sure how many New Zealand teachers might return and principals were worried about the likely lack of foreign teachers.
"I was at a meeting on Friday and there was some talk about 'gee what are we going to do next year?' because we all have been recruiting quite heavily from overseas in recent years and if that avenue is cut off we are a little bit worried about being able to fully staff our schools at the beginning of 2021."
Minister of Education Chris Hipkins reiterated the possibility of New Zealand teachers returning home, but acknowledged that was based on anecdotes and there was no data available now to support that assumption.
"New Zealand teachers are actually in very high demand around the world and they're very likely to want to come home in the current environment," Hipkins told Morning Report.
"One of the challenges we've had is data has not been great on teacher supply, it's largely been left to schools to sort that out. We've compiled much better data now about a number of qualified and registered teachers we have in New Zealand, the number we think we're going to need in future years and the numbers coming out of training."
Hipkins said there was "no doubt there is a brewing shortage of secondary school teachers that we need to get on top of", but added that the projections suggested the shortage of primary school teachers peaked a year ago and was still a few years away for secondary school teachers.
"Schools have found ways to make things work even if they have had difficulties filling all of the vacancies they've had, and that's including just rearranging timetables and doing a variety of innovative things, in the worst case scenario they can use Te Kura - the correspondence school ... if they can't find a subject specialist teacher."
The ministry was focusing on recruiting new trainees, he said, but teachers were still going to have to find a way around the problem for another few years yet.
In the meantime, New Zealanders in the country whose registration had lapsed would also be provided with free refresher training if they wished to re-enter the field, he said.
Border exemptions for teachers not ruled out - Hipkins
Auckland Primary Principals Association president Stephen Lethbridge said schools were in a staffing crisis and too few teachers were graduating from initial teacher education (ITE) programmes to fill their vacancies.
"There's some pretty low numbers of graduates graduating from ITE programmes and they are being snapped up really quickly in the mid-year intakes so the worry that schools have is how are we going to keep our children with teachers if we can't access overseas-trained teachers," he said.
Lethbridge said it was possible that more New Zealand teachers would return because of the pandemic, but schools would still need foreign teachers.
"If we're looking for foreign teachers coming in, we would need to think about having something in place for the start of next year," he said.
Education Minister Chris Hipkins said the government was looking at increasing the capacity of the quarantine system but gave no indication of when foreign teachers might be allowed in.
"At this point, the biggest constraint we've got is quarantine and managed isolation. We only have so many beds available and we know we've got a number of New Zealand citizens and residents wanting to return home, they've got a right to return home so naturally, they get the first priority for those beds that are available," he said.
"There are a number of other groups that sit high on the priority list once we're through that and of course groups like teaching, where there are critical shortages, those are the sorts of groups that will be high on the priority list when we're in a position to be able to bring extra people in."
He told Morning Report he was not ruling out exemptions for teachers at this stage.
"The peak of our potentially incoming teachers wouldn't be until January, teachers are certainly high on priority list of people who are next on the returning list after citizens."